The purpose of this weekly seminar is to study several research papers on the geometry of Shimura varieties mod p as well as arithmetic applications, and hopefully forming new research ideas. All talks will be given by participants, and each meeting will be about 120 minutes, consisting of 90 minutes lecture (with 10 minutes break in the middle) and 20 minutes discussion.
Caveat:In order to protect our common intellectual property rights, these original results should not be made public for the time being. You should therefore keep all videos and notes in a safe place to prevent disclosure.
(2/28) Wenhan Dai: Splitting models for U(2)-Shimura varieties (Hilbert case was discussed in [RX], please modify the discussion into the setup of U(2)-Shimura varieties). (video)
(3/6) Deding Yang: Ampleness criterion for automorphic line bundles on U(2)-Shimura varieties, I [Yang]. (video)
(3/13) Deding Yang: Ampleness criterion for automorphic line bundles on U(2)-Shimura varieties, II [Yang]. (video)
(3/20) Haocheng Fan: Irreducibility of nonordinary strata on U(2,1)-Shimura varieties mod p [Fan]. (video)
(3/27) Haocheng Fan: Overflow of the last talk. (video)
(3/27) Qijun Yan: Galois representations associated to cohomology of automorphic line bundles on Hilbert modular varieties, I [ERX]. (video)
(4/3) Qijun Yan: Galois representations associated to cohomology of automorphic line bundles on Hilbert modular varieties, II [ERX]. (video)
(The meeting is canceled during the PKU spring holiday.)
(5/8) Ruiqi Bai: An example of stratifications on unitary Shimura varieties. (video)
(5/15) Qijun Yan: Galois representations associated to cohomology of automorphic bundles on Shimura varieties of Hodge type, I [GK]. (video)
(5/22) Qijun Yan: Galois representations associated to cohomology of automorphic bundles on Shimura varieties of Hodge type, II [GK].
(5/29) Wenhan Dai: Description of strata for splitting model of U(2)-Shimura varieties mod p. (video)
(6/12) Qijun Yan: Galois representations associated to cohomology of automorphic bundles on Shimura varieties of Hodge type, III [GK]. (video)
(6/19) Zeyu Wang: Hecke operators on coherent cohomology of unitary Shimura varieties, I [FP]. (video)
(6/26) Zeyu Wang: Hecke operators on coherent cohomology of unitary Shimura varieties, II [FP].
Readme:The link for recordings of this seminar series are perennially valid. The password is ??77, where the first two characters denote the ring of integers of our imaginary quadratic extension field.
References
[Chai-Oort] C.-L. Chai and F. Oort, Monodromy and irreducibility of leaves, Ann. of Math.173 (2011), 1359–1396.
[ERX] M. Emerton, D. Reduzzi, and L. Xiao, Galois representations and torsion in the coherent cohomology of Hilbert modular varieties, Crelle726 (2017), 93–127,
[Fan] H. Fan, work in progress.
[FP] N. Fakhruddin and V. Pilloni, Hecke operators and the coherent cohomology of Shimura varieties, Journal de l’IMJ (2021), 1–69.
[GK] W. Goldring and J.-S. Koskivirta, Strata Hasse invariants, Hecke algebras and Galois representations, Invent. Math.217 (2019), 887–984.
[RX] D. Reduzzi and L. Xiao, Partial Hasse invariants on splitting models of Hilbert modular varieties, Ann. Sci. de l’ENS50 (2017), 579–607.